Since last two days I am facing this issue in HTC 8X, please help me to fix this issue
I have experienced similar issues on a Lumia 1520 device. Make sure that the date and time is set correctly. Some devices apparently have issues maintaining a synchronized clock when their battery depletes.
Check to make sure that you phone has background data enabled.
Check to see that your phone is not blocking background data to your email service.
Check to make sure the phone loads fewer messages and that it loads in shorter intervals.
If none of those things are work check to make sure that your email is not blocking messages from being set to your device.
I know gmail will sometimes not authorize your device sighting security issues.